It's tempting to say they can take down things like fake election dates without causing any concern, and that's probably true. But there also isn't much that falls in that category, and people can still send such messages via other messaging platforms like WhatsApp, email, the web etc. So it may simply not be worth the slippery slope in the end.
I would also add that part of the worldview has to do with fear of coercion. I don't profess to know how to fight conspiracy theories in general, but if I was tasked with doing it I'd be very wary about using coercion as a method. Streisand effect.
And yes, I get that your response is going to be something of the form "But how do you KNOW Facebook is actually right?". And again I point out that this is a practical problem and that the subject we are talking about is vaccines (about which you agree, right?), not an abstract idea of Facebook-blessed truth.
Tbh I have not done the research but I have no doubt there have been faulty or problematic vaccines at one time or another. Just like any other medical treatment there is a chance rhat they have defects, cause side effects, followed bad quality control protocol. Elevating vaccines to this status of being not allowed to be critisized for fear of our society being damaged seems like an almost equally dangerous alternative to what we have now. If people are legitimately hurt by a vaccine, they have a right to have a voice, and we have a responsibility as a society to hold those at fault accountable. That can't happen if we treat every person on facebook with even the slightest grievance about a vaccine like they are insane.
And to address your point on practicality; the fact of the matter is, anti-vax movements have never been normalized. There is enough pressure from employers, schools, government, and scientists that most people will get vaccinated if it is found to be of personal or public benefit. Hardcore antivaxers are generally looked down upon by the public.